First measurement of the total gravitational quadrupole moment of a black widow companion

We present the first measurement of the gravitational quadrupolemoment of the companion star of a spider pulsar, namely the black widow PSR J2051.0827. To this end, we have re-analysed radio timing data using a new model that is able to account for periastron precession caused by tidal and centrifugal deformations of the star as well as by general relativity. The model allows for a time-varying component of the quadrupole moment, thus self-consistently accounting for the ill-understood orbital period variations observed in these systems. Our analysis results in the first detection of orbital precession in a spider system at ω˙ = -68+0°.9-0°.5 yr-1 and the most accurate determination of orbital eccentricity for PSR J2051.0827 with e=(4.2±0.1)×10-5. We show that the variable quadrupole component is about 100 times smaller than the average quadrupole moment Q¯ = -2.2+0.6-1 × 1041 kgm2. We discuss how accuratemodelling of highprecision optical light curves of the companion star will allow its apsidal motion constant to be derived from our results.